To make a car move without touching it you can use magnetic forces like using a magnet to pull the car along a surface.
Placing the car on a downward slope can allow the car to also move without touching it other than you needing to touch it to place it near the downward slope.
Once the car is placed on the downward slope or hill, the car will go down the hill by itself due to gravity pulling it down the slope.
Placing the car on a downward slope, allows the car to be pulled forward and down the slope through gravity without any extra effort.
For toy cars to move them without touching you can also attach a balloon to the car and when the air escapes the balloon, the action reaction force called Newton's Third Law will move the car forward.
You can also attach a magnet to a toy car and use another magnet that is handheld to push the car forward by facing the same poles of the magnet toward each other which is North-North or South-South.
Attracting forces use a magnet to pull the car along a surface, although it works best on smooth surfaces.
You can also use rubber bands on toy cars to make them move without touching them.
You can use rubber bands connected to the axles of the toy cars and when you pull back or twist the rubber bands it stores energy and releases the stored energy to propel the car forward.
You can also tie a string to the car axle and wrap it around and pull the string can to propel it.
If you need to move a regular car or real car without touching it you can use gravity to allow the car to roll down a slight incline in neutral.
Or if the car has no wheels, you can use car dollies or casters to move them.
Placing heavy duty hydraulic wheel dollies under each tire of the car to lift the car and allowing it to be rolled easily without touching the car body itself is also a good way of moving the car without touching it.